Unitary part of a contraction

Hwa Long Gau, Pei Yuan Wu

研究成果: 雜誌貢獻期刊論文同行評審

5 引文 斯高帕斯(Scopus)


For a contraction A on a Hilbert space H, we define the index j (A) (resp., k (A)) as the smallest nonnegative integer j (resp., k) such that ker (I - Aj * Aj) (resp., ker (I - Ak * Ak) ∩ ker (I - Ak Ak *)) equals the subspace of H on which the unitary part of A acts. We show that if n = dim H < ∞, then j (A) ≤ n (resp., k (A) ≤ ⌈ n / 2 ⌉), and the equality holds if and only if A is of class Sn (resp., one of the three conditions is true: (1) A is of class Sn, (2) n is even and A is completely nonunitary with {norm of matrix} An - 2 {norm of matrix} = 1 and {norm of matrix} An - 1 {norm of matrix} < 1, and (3) n is even and A = U ⊕ A, where U is unitary on a one-dimensional space and A is of class Sn - 1).

頁(從 - 到)700-705
期刊Journal of Mathematical Analysis and Applications
出版狀態已出版 - 15 6月 2010


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